On the fractal dimension of the Henon attractor

We re-measured the fractal dimension of the Hénon attractor by direct box-counting. We paid special attention to (a) optimal speed and use of storage, and (b) systematic corrections due to the finiteness of the number of iterations. Covering with grids of up to 9600 × 9600 boxes, we observe that the number N(?, n) of boxes visited after n iterations obeys a scaling law N(?, ∞) - N(?, n) ≈ const × ?^-αn^-β (for n → ∞) with α = 2.42 ± 0.15, β = 0.89 ± 0.03. Using this extrapolate to n → ∞, we obtain D = 1.28 ± 0.01 in disagreement with previous box-counting estimates, but in agreement with a recent indirect evaluation.